A walk through of the JWST PandExo (Pandeia ETC for Exoplanets) for the NIRCam Grism Time Series Science Use Case is provided, demonstrating how to select exposure parameters for this observing program.

Introduction

PandExo is the "ETC ('Pandeia') for Exoplanets" which performs signal-to-noise (SNR) calculations for the JWST time series observing modes. The calculations from the JWST Exposure Time Calculator (ETC, which uses "Pandeia") are considered to be conservative (and averaged over wavelengths) SNR estimates for the exoplanet transit/eclipse depths or brown dwarf rotation amplitudes.

The ETC includes an error term for residual flat field errors which affects long exposures, and significantly underestimates the SNR for exoplanet transit spectroscopy where we take relative measurements. For exposures longer than ~10,000s, ETC calculations have a "noise floor" above which an increase in exposure time no longer results in an increase in SNR that scales with the square root of the exposure time. Since we are making relative measurements on the same pixels for exoplanet transit spectroscopy, our precision is not affected by the "noise floor" imposed by the residual flat field errors. The NIRCam Grism Time-Series Observations of GJ 436b provides this conservative, average estimate, but using the JWST ETC to compute a full exposure with 5764 integrations is not yet possible for time series observations (TSOs).

For the "NIRCam Grism Time-Series Observations of GJ 436b", we focus on selecting stellar, planetary, and exposure parameters to detect the exoplanet transit at the desired signal-to-noise ratio (SNR), for each wavelength. We start by defining the stellar, planetary, observational, and instrument modes specific to the proposal observations. The result of these calculations will be both the expected SNR on the host star and exoplanetary atmospheres, as well as necessary parameters to input into the Astronomer's Proposal Tool (APT) observation template, which is used to specify an observing program and submit proposals.

Observing goals of time series observations

The scientific measurement for an exoplanet transit is the "transit depth", which is a temporal measurement. The spectroscopic result is therefore a relative comparison between a contiguous sequence of time-series measurements, (i.e., transit depth over wavelength). It is equivalent to measuring variations in the stellar spectrum over time.

Our goal in this example is to achieve a relative precision of ~50 parts per million (ppm) on the transit depth per "spectral bin" or "channel," after subtracting the primary transit from the out-of-transit data. Atmospheric models (see PandExo) predict that this should provide a useful signal-to-noise on the exoplanet atmospheric spectroscopic signal (~100-250 ppm). A "spectral bin" or "channel" is a set of pixels across the spectrum that we will combine ("bin") to maximize the temporal precision per spectroscopic channel.

To maximize the relative precision between the in-transit and out-of-transit flux (over time), we need to observe the science target long enough to observe the transit, plus a window of time before and after the transit. For this source, the transit duration is 0.76 hours. We will therefore choose a transit window of 3.27 hours (11772 s), which is 3 times the transit duration + 1 hour—for "detector settling" (see Noise Sources for Time-Series Observations).

Opening PandExo

After opening the PandExo website, select "New Calculation" under the picture of "James Webb Space Telescope".

At the top of the next page, it is useful to set the name of the target in the "Name" text box. This will become relevant on the next page, which will have a list of all recent calculations from the current computer.

Setting planetary parameters in PandExo

Temperature (K) to 1000 K (The equilibrium temperature for GJ436b is 712 K)

Select Chemistry Type to Equilibrium Chemistry

Clouds or Scattering to Weak Rayleigh

Planet Mass to 22.2 ME (relative to Earth mass)

Planet Radius to 4.327 RE (relative to Earth radius)

Stellar Radius to 0.42 RS (relative to Solar radius)

Figure 3 shows a screenshot of the planetary parameters input page in PandExo.

Figure 3. Planetary bulk and atmospheric properties

Nominal input planetary parameters for PandExo to make an accurate prediction for observing GJ 436 with JWST NIRCam Grism Times Series..

Setting transit observational parameters in PandExo

We need to supply the observational parameters for GJ 436b and encompass the entire transit and necessary out of transit time to make the relative measurement. For this, we need to set the following parameters (Figure 4):

Nominal input detector parameters for PandExo to make an accurate prediction for observing GJ 436 with JWST NIRCam Grism Times Series with the F444W filter.

Run PandExo

To compute all of the necessary—and useful—values for planning and proposing for JWST TSO observations, select the "Submit" button at the end of the page. This operation could take a few minutes. The following page will provide a rotating symbol and the label "Running" if the calculations are ongoing. Moreover, the buttons to the right (a box and an eye) will be grey and unusable.

After the calculation has finished processing on STScI server, the rotating dial will stop and the label "Running" will change to "Finished". Moreover, the buttons to the right are now useful.

PandExo results

After selecting the EYE symbol, the first image that we can see is the raw, unbinned planetary spectrum as it would be resolved by fitting a transit model (see Kreidberg 2015) to the synthetic JWST NIRCam simulated observations, which include photon noise, background noise, and read noise as is expected from both Pandeia and field testing of the instruments (Figure 6).

There are 2 dials to this plot, as well as the standad Bokeh interaction functions (e.g. move, zoom, etc): "binning" and "Num trans". The units of "binning" selection are given in the log10 (min(wavelengths per bin)); the default is at the native resolution for NIRCam (R~1600), such that log10 (1.6/1600) = -3.301. The scientific measurement for an exoplanet transit is the "transit depth" or "eclipse depth", which is a temporal measurement. The spectroscopic result is therefore a relative comparison between a contiguous sequence of time-series measurements – i.e. transit/eclipse depth over wavelength. It is equivalent to measuring variations in the stellar spectrum over time.

The native resolution can provide a useful transmission/emission spectrum, if the atmospheric signal is large enough to overcome the intrinsic, temporal noise, which is dominated by the photon noise and read noise. It is much more common to "bin" the native spectrum into what are called "channels", which are higher SNR sets of pixels that improve the SNR on the temporal signal. In our case, we will bin 20 pixels together to form ~100 "channels" (i.e., 2048 pixels / 20 (pixels per bin)), which results in a binned resolution of R~80. Sliding the dial to 1.70103 (=log10 (1.6/80)), is equivalent to binning by 20 pixels per channel. The plot itself will update to reveal what this binning should look like from our synthetic observation. This dial allows the user to visually determine ithe theoretical spectrum (here: clear, equilibrium chemistry) with the precise stellar model for the GJ 436 system.

Figure 7 shows a zoom in of the binned spectrum using the Bokeh tools on the right side of the interactive plot.

Figure 7. Zoom-in of binned spectrum GJ 436b

1D stellar and error spectra for GJ 436

Scrolling down on this page, we come to the 1D stellar and error spectra for GJ 436. The first tab on the top figure defaults to "Total Flux" (Figure 8), which shows the integrated electrons per wavelength, integrated to form the 1D stellar spectrum (top) and 2D spectral image (bottom).

Selecting the SNR tab at the top of the upper figure reveals the SNR expected per wavelength along the stellar spectrum (Figure 9). Because our exoplanet host stars are nominally bright, the stellar spectrum is very nearly photon noise limited; the SNR figure is therefore precisely the √(1D stellar spectrum) over wavelengths.

Transit/Eclipse depth uncertainty over wavelengths

The final tab to select on this figure is likely the most important. Select the "Error" tab to see the predicted ppm uncertainty as a function of wavelength (Figure 10).

Figure 10. Predicted uncertainty in spectrum as a function of wavelength

Figure 10 shows that the smallest uncertainty predicted for GJ 436 in our observational parameters is, on average, close to 150 ppm. This estimate is for the native resolution (R~1600); because we are expecting to bin the 2D image by 20 columns to form 100 channels from 2048 columns, we will state that we predict to achieve 150/√20 ~ 33 ppm uncertainty (on average) across the spectrum.

Determining number of groups and number of integrations

APT requires the user to enter the number of groups (NGroups) and number of integrations (NIntegrations) to define the length of the exposure. We want to observe a balanced number of groups per integration to maximize both temporal resolution and spectral precision. Previous experience has led the community to nominally fill the detector pixel wells to an average of half full. Because an H2RG pixel can hold ~65k electrons, we nominally choose ~30k electrons per pixel per integration. In the context of number of groups for JWST, PandExo derives the number of groups corresponding to the onset of saturation (NGroupssat) (we defined this at 80% well depth), and then selects the number of groups per integration to be NGroupssat/2 (rounding up).

After the "Table of Original Inputs"—which matches the values we entered at the beginning—there is a second table named "Timing Info" (Figure 12).

Figure 12. The "Timing Info" table contains all of the necessary information that APT requires to derive the exposure parameters (NGroups and NIntegrations)

PandExo warnings

The final table provided by PandExo is named "Warnings" (Figure 13). If the target is not too bright for the minimum number of groups (NGroupsmin = 2), and the given instrument/detector setup, then all "values" should be listed as "All Good." If the any pixels on the detector are saturated, or experience strong non-linearity, then one of these warnings will list further information.

"Group Number Too Low" warns if the target is too bright for the minimum number of groups.

"Group Number Too High" warns if the target is too faint for the maximum number of groups.

"Non linear?" warns if any pixels are expected to sustain significant non-linearity, which could happen if the target is not too bright to saturate pixels, but bright enough to sustain non-linearity.

"Saturated?" warns if any pixels are expected to be saturated.

"% full well high" warns if the definition of full well provided on the previous page is useful to achieve nominal integration parameters.

"Num groups Reset" is a catch all warning that warns if the "something else went wrong", which might have required PandExo to reset the number of groups to the minimum value of 2.

Figure 13. Warnings table in PandExo

This final PandExo table warns the user if any problems were encountered in the simulation, as described in the main text. If the simulation ran without any issues, "All good" will be listed in the "Value" column.

Download data

PandExo provides a "Download Data" button at the bottom of the results page, which allows the user to download a `pickle` file for the user to use Python to plot and interact with all of these figures. The follow code snippet would allow user to create the "Error Spectrum" figure above – with Python 3.6.1 :: Anaconda 4.4.0 (×86_64):

# To plot the error spectrum after downloading the PandExo results

importpickle

frompylabimport *; ion()

id ='f539d647-843e-44e2-9c5e-007704ea8201e' # this `id` only applies for this test case; all users will have a different values for `id`